2003

最新文章

• Finiteness of Selmer groups and deformation rings AI翻译
  作者：Khare, C; Ramakrishna, R
  作者单位：Tata Institute of Fundamental Research (TIFR); Utah System of Higher Education; University of Utah; Cornell University
• Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps AI翻译
  作者：Przytycki, F; Rivera-Letelier, J; Smirnov, S
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; State University of New York (SUNY) System; Stony Brook University; Royal Institute of Technology
  摘要：We show equivalence of several standard conditions for non-uniform hyperbolicity of complex rational functions, including the Topological Collet-Eckmann condition (TCE), Uniform Hyperbolicity on Periodic orbits, Exponential Shrinking of components of pre-images of small discs, backward Collet-Eckmann condition at one point, positivity of the infimum of Lyapunov exponents of finite invariant measures on the Julia set. The condition TCE is stated in purely topological terms, so we conclude that ...
• Entropy and the combinatorial dimension AI翻译
  作者：Mendelson, S; Vershynin, R
  作者单位：Australian National University; University of Alberta
  摘要：We solve Talagrand's entropy problem: the L-2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley's theorem on classes of {0, 1}-valued functions, for which the shattering dimension is the Vapnik-Chervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of K. This has a numbe...
• Global uniqueness for an inverse boundary value problem arising in elasticity (vol 118, pg 457, 1994) AI翻译
  作者：Nakamura, G; Uhlmann, G
  作者单位：Hokkaido University; University of Washington; University of Washington Seattle
• Morse theory on spaces of braids and Lagrangian dynamics AI翻译
  作者：Ghrist, RW; Van den Berg, JB; Vandervorst, RC
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Nottingham; Vrije Universiteit Amsterdam; University System of Georgia; Georgia Institute of Technology
  摘要：In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease their topological complexity; algebraic lengths decrease monotonically. This topological invariant is d...
• Nilpotent commuting varieties of reductive Lie algebras AI翻译
  作者：Premet, A
  作者单位：University of Manchester
  摘要：Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p greater than or equal to 0, and g = Lie G. In positive characteristic, suppose in addition that p is good for G and the derived subgroup of G is simply connected. Let N = N(g) denote the nilpotent variety of g, and C-nil(g) := {(x,y) is an element of N x N \ [x, y] = 0}, the nilpotent commuting variety of g. Our main goal in this paper is to show that the variety C-nil(g) is equidimensional....
• On the first Witt index of quadratic forms AI翻译
  作者：Karpenko, NA
  作者单位：Universite de Lille
  摘要：We prove Hoffmann's conjecture determining the possible values of the first Witt index of anisotropic quadratic forms of any given dimension. The proof makes use of the Steenrod type operations on the modulo 2 Chow groups constructed by P. Brosnan.
• Algebraic Morava K-theories AI翻译
  作者：Borghesi, S
  作者单位：Universite Paris Saclay
  摘要：For any prime q and positive integer t, we construct a spectrum k(t) in the stable homotopy category of schemes over a field k equipped with an embedding k --> C. In classical homotopy theory, the C realization of k(t) is known as Morava K-theory. The algebraic content lies in the fact that these spectra are defined as the homotopy limit of a tower whose cofibers are appropriate suspensions of the motivic Eilenberg-MacLane spectra, which are known to represent motivic cohomology in the stable ...
• Toroidal varieties and the weak factorization theorem AI翻译
  作者：Wlodarczyk, J
  作者单位：Purdue University System; Purdue University
  摘要：We develop the theory of stratified toroidal varieties, which gives, together with the theory of birational cobordisms [73], a proof of the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field K of characteristic zero is a composite of blow-ups and blow-downs with smooth centers.
• Smooth points of T-stable varieties in G/B and the Peterson map AI翻译
  作者：Carrell, JB; Kuttler, J
  作者单位：University of British Columbia; University of Basel
  摘要：Let G be a connected semi-simple algebraic group defined over an algebraically closed field k, and let T subset of B subset of P be respectively a maximal torus, a Borel subgroup and a parabolic subgroup of G. Inspired by a beautiful result of Dale Peterson describing the singular locus of a Schubert variety in G/B, we characterize the T-fixed points in the singular locus of an arbitrary irreducible T-stable subvariety of G/P (a T-variety for short). Peterson's result (cf. The Deformation Theo...